In this work, we introduce two simple transport models to evaluate the time evolution of electron temperature and density profiles during sawtooth cycles (i.e. over a sawtooth period time-scale). Since the aim of these simulations is to estimate reliable profiles within a short calculation time, two simplified ad-hoc models have been developed. The goal for these models is to rely on a few easy-to-check free parameters, such as the confinement time scaling factor and the profiles' averaged scale-lengths. Due to the simplicity and short calculation time of the models, it is expected that these models can also be applied to real-time transport simulations. We show that it works well for Ohmic and EC heated L- and H-mode plasmas. The differences between these models are discussed and we show that their predictive capabilities are similar. Thus only one model is used to reproduce with simulations the results of sawtooth control experiments on the TCV tokamak. For the sawtooth pacing, the calculated time delays between the EC power off and sawtooth crash time agree well with the experimental results. The map of possible locking range is also well reproduced by the simulation.